Another idea is memorialize the GlobalIDs in the Feature Class (create new field called [GBL_GUID], GUID type --> Field Calculate the [GBL_GUID] field to the values in GlobalID). Now, if you export any data from that Feature Class in whatever database format.. the relationship will be maintained through the new [GBL_GUID] field.
After further testing, Mitch's solution won't work for us. The GUID field created doesn't autopopulate with a GUID in either ArcMap nor ArcGIS Online once deployed. Unless there is another trick to it, I'll have to stick to my original solution.
Will since you have an EGDB.....this is another one of those "Tech support will disown you" hacks #if they catch you doing it but...
In SQL Management Studio, change the object_flags to 4 (from 256) and sde_type to 14 (from 12) for the GlobalID column in SDE_column_registry for both feature classes. Then do you move. Remember to change them back!
very handy! I wonder if this can be mixed with some other python tools for archiving and downloading between AGOL and on-premise databases to achieve a true "two-way" sync without having to rely on flaky portal or pay for a data interop license.